Detailed Evidence for Flare-to-Flare Variations of the Coronal Calcium ...

THE ASTROPHYSICAL JOURNAL, 501 : 397È407, 1998 July 1 ( 1998. The American Astronomical Society. All rights reserved. Printed in U.S.A.

DETAILED EVIDENCE FOR FLARE-TO-FLARE VARIATIONS OF THE CORONAL CALCIUM ABUNDANCE J. SYLWESTER Space Research Centre, Polish Academy of Sciences, ul. Kopernika 11, 51-622, Wroclaw, Poland ; js=cbk.pan.wroc.pl

J. R. LEMEN Lockheed Martin Solar and Astrophysics Laboratory, H1-12 B/252, 3251 Hanover Street, Palo Alto, CA 94304 ; lemen=sag.space.lockheed.com

AND R. D. BENTLEY, A. FLUDRA,1 AND M.-C. ZOLCINSKI Mullard Space Science Laboratory, Holmbury Saint Mary, Dorking, Surrey, RH5 6NT, United Kingdom Received 1997 September 2 ; accepted 1998 February 9

ABSTRACT The analysis of X-ray solar Ñare spectra obtained by the Bent Crystal Spectrometer on board the Solar Maximum Mission satellite is presented. The ratio of the Ca XIX resonance line intensity to the nearby continuum is used to measure the calcium abundance relative to hydrogen (A ). A description of Ca the spectroscopic method of determining the absolute calcium abundance is given. Possible instrumental and solar e†ects that might inÑuence the abundance estimates are evaluated. Over 5000 spectra from more than 100 Ñares are analyzed. We Ðnd a Ñare-to-Ñare variation for A that is not correlated with Ca observed from two active Ñare size, Ha importance, or with several other Ñare characteristics. For Ñares regions, the observed value of A increases as a function of time. The average for all Ñares is SA T \ Ca of investigated correlations of derived A values with severalCaÑare (5.77 ^ 1.41) ] 10~6. A discussion Ca characteristics is presented. Subject headings : Sun : abundances È Sun : corona È Sun : Ñares È Sun : X-rays, gamma-rays 1.

INTRODUCTION

For investigations that are made in the X-ray or EUV, there are several considerations : (1) the line intensities must be accurately determined, (2) the atomic data must be accurately known in order to calculate the synthetic spectra which are Ðtted to the observations, and (3) the conditions of the emitting solar plasma with regard to various assumptions such as thermal equilibrium must be evaluated. It is relatively easy to accommodate for these considerations in the analysis of X-ray or EUV spectra, contrary to the analysis of spectra from the visible range. In an earlier analysis on a limited set of data from the NASA Solar Maximum Mission (SMM) (Sylwester, Lemen, & Mewe 1984 ; Lemen, Sylwester, & Bentley 1986 ; Fludra et al. 1991), we were the Ðrst to point out the presence of Ñare-to-Ñare variations of A from spectroscopic studies. Ca data were done by Fludra More recent analyses of calcium et al. (1993) and Bentley, Slywester, & Lemen (1998), who derived A using data from the crystal spectrometer on the Japanese CaY ohkoh satellite, and Sterling, Doschek, & Feldman (1993), who studied data obtained with the SOLFLEX instrument on P78-1. In order to obtain absolute abundances, the latter authors normalized their results to the SMMÈBent Crystal Spectrometer continuum observations. In this work, observations of the line and continuum obtained with the same spectrometer are analyzed. In this paper, we present a method of determining the absolute calcium abundance relative to hydrogen using the data acquired from Ñare plasmas observed with the Bent Crystal Spectrometer (BCS) on board SMM. The SMM-BCS was one of two spectrometers constituting the X-Ray Polychromator experiment (Acton et al. 1980). We investigate the Ñare-to-Ñare variations of the Ca XIX resonance line (w) intensity, 1S È1P at 3.178 A , relative to the 1 nearby continuum (Veck &0Parkinson 1981 ; Sylwester et al. 1984). The values of A are determined for 146 Ñares during the decay phase.CaContrary to the case for photo-

The determination of absolute elemental abundances is one of the fundamental problems of astrophysics. The composition of the solar plasma is one of the primary sources of information for the cosmic elemental abundances. Several spectroscopic methods, covering a wide range of the electromagnetic spectrum, are available for determination of solar abundances. At optical wavelengths, photospheric abundances can be determined from the ““ equivalent widths ÏÏ of the Fraunhofer absorption lines of neutral, singly, and doubly ionized atoms (Athay 1986). Chromospheric and low corona abundances may be determined from observations of permitted UV emission lines from various ionization stages (Pottash 1964 ; Mariska 1980 ; Widing & Feldman 1989). Coronal abundances have been derived from the analyses of the solar X-ray and EUV spectra (Parkinson 1977 ; Veck & Parkinson 1981 ; Feldman 1992) or from optically forbidden emission lines of highly ionized species (Mason 1975 ; Arnaud 1984). In situ studies using spacecraft measurements have been made for the elemental composition of the solar wind (Geiss 1982 ; Geiss & Bochsler 1986) and solar energetic particles (Meyer 1985a, 1985b ; McGuire, von Rosevinge, & McDonald 1985 ; Stone 1989). Spectroscopic X-ray and EUV research over the past 10 years strongly indicates that the elemental abundances in the solar corona di†er from photospheric values (Feldman 1992 ; Meyer 1993). The compositional di†erences may be organized in terms of the Ðrst ionization potential (FIP). Elements with FIP less than 10 eV were observed to be more abundant in the corona (by up to an order of magnitude), with the abundance varying from time to time and from coronal structure to structure. 1 Current affiliation : Rutherford Appleton Laboratory, Astrophysics and Geophysics Division, Chilton, Didcot, Oxfordshire OX11 0QX, United Kingdom.

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spheric abundance studies, coronal abundances are generally not measured relative to hydrogen ; only ratios of heavy elemental abundances are normally obtained. The only way to measure the ratio of heavy elemental abundances relative to H is to make use of the line-to-continuum ratio. The Ca XIX w line is a particularly good choice for abundance determinations because the intensity ratio of this line relative to the nearby continuum varies only weakly with temperature ; thus, estimates of abundance may be reliably obtained within the isothermal approximation. The Ca XIX line is very bright in solar Ñare spectra, and so its intensity can be easily measured. Theoretical calculations are available for the complex of Ca XVIIIÈXIX near j \ 3.2 A . The spectral Ðtting makes use of a semiempirical determination of the Ca XIX fractional ionization as derived by Lemen et al. (1998). 2.

THE BENT CRYSTAL SPECTROMETER

The BCS is one of two X-ray spectrometers that make up the X-Ray Polychromator (XRP) instrument. The SMM-BCS consists of a collimator, eight curved germanium crystals, eight one-dimensional position-sensitive sealed proportional counters, detector ampliÐers, and processing and control electronics. The multigrid collimator had a 6@ ] 6@ FWHM triangular response in two directions, parallel and perpendicular to the dispersion axis ; the dispersion axis was parallel to the east-west direction on the Sun. The collimator resolution is sufficient to isolate the Ðeld of view to an individual active region on the Sun. The observing target was selected by pointing the SMM spacecraft using ground control commands. The SMM-BCS observed the helium-like Ca XVIIIÈXIX lines near 3.2 A in one channel and various highly ionized iron transitions near j \ 1.9 A in the other seven channels. A typical calcium Ñare spectrum is shown in Figure 1. The principal lines are labeled : the resonance line (1s2 1S È1s2p 1P ) as w, the intercombination lines (1s2 1S È1s2p 3P0 ) as 1 0 y and x, and the forbidden line (1s2 1S È1s2p 3S )1,2 as z. 0 1

FIG. 1.ÈExample of a Ca XVIIIÈXIX spectrum recorded by SMM-BCS from the decay phase of the Ñare on 1980 June 29 at 10 : 48 UT ; the integration time was 23 s. The minimum threshold for detection with this spectrometer is T [ 7 MK, EM [ 5 ] 1047 cm~3. The principal line features are labeled and explained in the text. The thermal continuum is seen at the short wavelength side of the resonance line and longward of the j, z line complex. The insert shows the time history of the count rate integrated over all wavelengths for this Ñare, and the arrow marks the time of the displayed spectrum.

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Besides these main spectral features, numerous blended satellite lines [e.g., k, 1s22p 2P È1s2p2 2D ; q, 1s22s 1@2 3@2 2S È1s2p(1P)2s 2P ] contribute to the observed spec1@2 3@2 trum. Low background count rates together with high spectral resolution (j/dj B 3450) permit the accurate determination of the line and continuum Ñuxes. The solar X-rays that enter the SMM-BCS through the multigrid collimator are dispersed by eight curved, germanium crystals (each approximately 15 cm long and 2.5 cm wide) into position-sensitive sealed proportional counters. The Ca XIX channel (channel 1) made use of the Ge 220 crystal plane. Because the crystals are curved, there are no moving parts in the spectrometer, but rather X-rays are dispersed along the position-sensitive proportional counters according to the Bragg di†raction condition : j \ 2d sin h ,

(1)

where 2d is the crystal spacing and j is the wavelength of the radiation refracted at the angle h. Because the crystal is curved, the Bragg condition is satisÐed for di†erent wavelengths along the length of the crystal. The position at which a photon is detected in the proportional counter is related to its incident energy. This type of spectrometer provides an advantage over spectrometers that scan a Ñat crystal if the spectra evolve rapidly, as during a solar Ñare. The SMM-BCS observes at all wavelengths simultaneously, and so there are no uncertainties about spectral evolution during the acquisition of a spectrum as there might be if the crystal is scanned over a range of wavelengths. The SMM-BCS has high sensitivity (e†ective area \ 0.024 cm2), and relatively short integration periods, of the order of tens of seconds, are required to obtain statistically acceptable spectra. The Ca XIX channel proportional counter had a 75 km thick beryllium window and was Ðlled with a mixture of noble gases. The average background level due to energetic particles was low, always less than 0.03 counts per wavelength bin per second, normally less than 1% of the observed continuum. During Ñight, Fe55 X-ray calibration sources were routinely exposed to the SMM-BCS detectors to monitor detector gain, and additional functional tests were carried out on a routine basis to monitor the linearity of the signal processing chain. All standard corrections resulting from the calibration data acquired in orbit have been applied to the SMM-BCS spectra in the course of our analyses. In the other SMM-BCS wavelength channels, an enhanced background is observed, contaminating the continuum, especially during the rise phase of Ñares. This is caused by the Ñuorescence of the germanium crystals by solar X-rays whose energies exceed the 11.1 keV ionization threshold of germanium (Parmar et al. 1981). Fortunately, the calcium spectrometer channel is free from this problem, since the pulse height discrimination of the processing electronics rejected all high-energy, nonsolar Ñux. The SMM-BCS instrument operated during 1980 FebruaryÈNovember in the Ðrst year of SMM operations and then again for several more years (1984È1989) following the in-orbit repair of the spacecraft. 3.

THE LINE-TO-CONTINUUM RATIO

The spectrum in the vicinity of Ca XIX, He-like X-ray triplet lines (resonance w, intercombination x, y, and forbidden z) includes blends of hundreds of satellite lines in

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where N and N are the electron and hydrogen number e H densities, respectively ; N /N \ 0.85 is assumed, which is e H appropriate for a fully ionized solar plasma. The e†ective excitation rates m (T ) are taken from the calculations of i Bely-Dubau et al. (1982), who take into account contributions from higher n satellite transitions. The ionization fraction is given by N /N . We use values for N /N i Ca Caxix Ca derived by Lemen et al. (1998) from semiempirical Ðts to SMM-BCS Ñare spectra. The photon Ñux per unit wavelength interval in the continuum can be expressed as F \ c

P

f (j, T )r(T )dT , c

(4)

where the emission function f (j, T ) for the continuum has c been taken from Mewe et al. (1986), who assume standard cosmic abundances of Allen (1973). Values of the continuum emission function depend only weakly on the plasma composition (see discussion in ° 6.4). The ratio of the w resonance line Ñux to the continuum at the wavelength of this line, j \ 3.178 A , can be calculated w from equations (2) and (4), assuming an isothermal plasma, as

FIG. 2.ÈExamples of F /F vs. T dependence are shown for two pairs c of Ñares with substantiallywdi†erent line-to-continuum values. Error bars indicate ^1 p uncertainties as determined from the least-squares spectral Ðtting procedure. As this data is taken from the Ñare decay, the time ordering of the data generally is from right to left in these Ðgure panels.

Ca XVIII (see Fig. 1). The upper states of the triplets are largely populated by direct excitation with some contributions from radiative recombination. The satellites are formed by inner shell excitation and dielectronic recombination. The photon Ñux for the calcium resonance emission can be shown to be optically thin for the case of the corona (see ° 6.2). The Ñux at the Earth (photon cm~2 s~1) in the emission line can be expressed as (Sylwester, Schrijver, & Mewe 1980b) F \A i Ca

P

f (T )r(T )dT , i

(2)

where r(T ) is the distribution of the emission measure over the temperature (di†erential emission measure) in the source. A is the abundance (relative to hydrogen) of Ca abundance is assumed to be uniform in the calcium. The emitting region. The emission functions f (T ) can be i expressed as N N i m (T ) , f (T ) \ (3.0 ] 10~28) e i i N N H Ca

(3)

F /F \ A f (T )/f (j , T ) , (5) w c Ca w c w where f (j , T ) is the continuum Ñux at the wavelength of c w w line. The ratios of F /F are shown as dashed the Ca XIX curves in Figure 2, where the valuew ofcA has been adjusted to Ðt the observations. One can see fromCathe plot that F /F w c varies by about a factor of 3 over the range of typical Ñare temperatures (8È20 MK). The relatively weak temperature dependence of this ratio means that errors in the temperature estimates of the spectra will introduce only a small uncertainty in the estimates for the calcium abundance. Furthermore, a weak dependence on temperature means that the introduction of an isothermal assumption will result in only a small error for the abundance determination (see ° 6.5). 4.

OBSERVATIONS

This study includes bright Ñares that were observed with the SMM-BCS in 1980, the Ðrst year of SMM operations, and during 1984È1987, the years following the in-orbit repair of the spacecraft. Flares in 1980 were selected from events whose integrated Ca XIX light curves had maximum count rates at the peak of the Ñare that were greater than 80 counts s~1. During the postrepair mission period (1984È 1987), Ñares listed in the XRP Team Final Report (Strong 1988) were selected that had greater than 100 counts s~1 at Ñare maximum. This criterion resulted in the identiÐcation of more than 250 Ñares. Some Ñares were subsequently eliminated because of data gaps. The present paper concentrates on Ñare decay phase data. There are several reasons for this. Generally, most Ñares as observed in hard and soft X-rays are seen to have a prompt energy release, sometimes accompanied by the acceleration of fast particles. In hard X-rays, the emission often appears to be nonthermal and intensity increases are often impulsive. During the decay phase, there is usually no hard X-ray emission, indicating that Ñare heating has ceased or is greatly reduced. As a result, the ionization state of the plasma is quasi-stationary (° 6.3) and plasma densities are higher, so one may neglect e†ects of transiently ionizing

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plasma. An isothermal approximation is also better during the decay phase. The absence of intense hard X-ray emission with energies greater than 11.1 keV lessens the danger of contamination of the thermal continuum from Ñuorescence of the germanium crystals. The continuum is assumed to be thermal and not a mixture of thermal and nonthermal emission. As the intrinsic line widths of the considered calcium transitions under low plasma density conditions are very small, the observed line widths are mainly determined by four factors : Doppler broadening, the instrument response function, the physical source size within the BCS Ðeld of view, and nonthermal plasma motions. The Doppler broadening is assumed to be Gaussian and is treated as a free parameter during the Ðtting procedure. The instrument spectral response function is characterized as a Voigt proÐle with corresponding Gaussian (FWHM \ 0.527 mA ) and Lorentzian (FWHM \ 0.612 mA ) components. The source size is limited by the actual Ñare size, which is generally much less than the size of the BCS collimator (FWHM \ 6@ ] 6@). During the decay phase, the nonthermal widths are small and directed Ñows are small (Fludra et al. 1989), which simpliÐes the line Ðtting. The observed line widths during the Ñare decay are dominated by Doppler broadening convolved with the instrumental response. Broadening due to other e†ects are less signiÐcant, but their possible presence has been accommodated by including an additional symmetric Gaussian component in the Ðtting process. From the original set of over 250 Ñares, 146 Ñares with good data during the decay phase were Ðtted to measure the line-to-continuum values. Included in our sample are 28 Ñares that were analyzed by Lemen et al. (1998) in order to determine a semiempirical value for the ionization fraction of N /N . More than 5000 spectra were Ðtted in total. Ca Ðt was examined visually, and unsatisfactory EachCaxix spectral cases were eliminated from the analysis. 5.

CALCIUM ABUNDANCE RESULTS

The calcium abundance was determined by Ðtting the theoretical value of the line-to-continuum ratio, F /F , to w c of the line-to-continuum observed during the decay phases our set of Ñares. The value of the resonance line intensity, F , and the continuum Ñux at line w are obtained in the w following manner. First, the spectrum is Ðtted with a complete spectral model, including all line blends and nearby satellites, in order to determine the best value of the electron temperature T and the isothermal emission measure. Under the assumption of an isothermal plasma, the emission measure / r(T )dT becomes EM \ / N2 dV , where / dV is e the volume of the emitting plasma. Values of F /F were w results, c computed (eq. [5]) from the Ðtted T and EM assuming for consistency the same A that was used in the Ðt. By these means, the intensity ofCaF itself can be estimated without the contribution of the wnearby dielectronic satellites. Systematic uncertainties in our derived theoretical values for F /F will lead at most to 20% errors in the w cof A (Lemen et al. 1998). In our synthetic estimated values model, the theoreticalCaspectra were convolved through the SMM-BCS instrument response function. The Ðtting code Ðts the resonance line (w) and wavelength region near the dielectronic satellite line (k). Further discussions about the Ðtting approach are given in Lemen et al. (1998), Fludra et al. (1989), and Lemen et al. (1984). The results of our Ðtting

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program have been compared with Antonucci et al. (1982), who use the same atomic data and are shown to be in relatively good agreement, except that the temperature values obtained by Antonucci et al. (1982) appear to be systematically lower by D1 MK. This is probably caused by the di†erent method of Ðtting spectra used by Antonucci et al. and their assumption that the thermal continuum is approximated as a constant in wavelength over the limited range of the SMM-BCS calcium spectrometer. In our Ðtting algorithm, the continuum spectrum is explicitly computed and a least-squares Ðtting method is used to chose the bestÐt parameters. However, the small di†erence in the estimated temperatures from the two Ðtting methods is not signiÐcant in terms of the present analysis, and the use of the Antonucci et al.Ïs results would have resulted in substantially the same estimates for the A . Ca The derived F /F values are shown for four Ñares in w c Figure 2 as data points. The values of F /F are plotted as a c the time order function of electron temperature T , andwthus of the measurements generally proceeds from right to left in the plot. The error bars represent 1 p uncertainties that are derived from the estimates of the goodness of Ðt by the spectral Ðtting code. The F /F curves for the two Ñares in w 1980 c the upper panel, observed on June 29 at about 10 : 44 UT and 1980 November 6 at about 17 : 28 UT, di†er by a factor of about 2, although their shapes as a function of temperature follow a similar trend. From equation (5), one interpretation for this behavior is that the calcium abundance relative to hydrogen is di†erent for the two cases. The values of A are estimated by Ðtting the predicted F /F to Ca F /F . The dashed curves are the wbest-Ðt c the observed w c values of F /F , where the value of A has been allowed to w result c vary. The Ðts in A \ (7.30 ^Ca 0.16) ] 10~6 for 1980 Ca A \ (3.40 ^ 0.09) ] 10~6 for June 29 at 10 : 44 UT and the Ñare on 1980 November Ca6 at 17 : 28 UT. The uncertainties in the measurements of the abundances come from the Ðts of the observed values of F /F to the theoretical w c both the uncervalues. These errors take into account tainties of temperature and continuum level determinations (see Lemen et al. 1998). The lower panel in Figure 2 gives two more examples of Ñares with signiÐcantly di†erent lineto-continuum values. The upper set of data was also taken from 1980 June 29 but from a Ñare that occurred later in the day at 18 : 26 UT, and the lower data set is for the Ñare that occurred on 1985 January 20 at 20 : 51 UT. The derived values of A for these two Ñares are (8.06 ^ 0.17) ] 10~6 and (5.15 ^Ca0.08) ] 10~6, respectively. Note that the uncertainties in the individual abundance measurements are much smaller than the Ñare-to-Ñare variations for these cases. In this analysis, it has been assumed that the calcium abundance remains constant during the decay phase of each Ñare. This assumption appears to be justiÐed by the fact that a comparison of many Ñares shows that most Ñares have approximately the same shape of observed F /F as a w cmore function of temperature (see Lemen et al. 1998 for details). In some cases, one or more additional heating episodes are observed during the decay phase ; these cases are treated as separate Ñares. When comparing Ñares with widely di†erent abundances, it is possible to visually identify the di†erence in the spectra. Figure 3 shows two spectra taken from the Ñares shown in Figure 2, plotted as histograms. The solid curves superposed on the observed spectra are the best-Ðt synthetic

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FIG. 3.ÈComparison of two spectra observed for Ñares with signiÐcantly di†erent F /F ratios. The solid curves superposed on the observed spectra are w c the best-Ðt synthetic spectra. The spectral Ðtting routine adjusts the electron temperature to match the temperature-sensitive intensity ratio of the dielectronic satellite line k to the resonance line w to the observed spectrum. These two spectra have nearly the same Ðtted electron temperatures and line widths. Note the di†erent values of the w line-to-continuum ratio that are seen for these two spectra. The inset is as in Fig. 1.

spectra. These two spectra were chosen because their Ðts resulted in nearly the same electron temperatures and line widths. The plot shows the di†erent resonance line-to-continuum ratios for these two Ñares. Table 1 summarizes the results for 146 Ñare decay phases. Included in the table is the NOAA active region number, the location on the solar disk of the Ñare, Ha and GOES X-ray Ñare classiÐcations, and number of spectra included in the determination of each abundance estimate. The values of A have been multiplied by 106 to facilitate the Ca table. The values labeled ^1 p are the uncerdisplay in the tainties that were described above. The times given represent the approximate peak of the Ñares as observed in the SMM-BCS. The average abundance for all 146 Ñare decay

phases is (5.77 ^ 1.41) ] 10~6. This is greater than the typically quoted photospheric value of A \ (2.6 ^ 0.4) Ca & Parkin] 10~6 or the coronal value determined by Veck son (1981) of A \ (3.2 ^ 1.2) ] 10~6 but is similar to the Ca of Sterling et al. (1993). value of 5 ] 10~6 The variation in the values of A is much larger than the Ca typical errors of the abundance determination, which supports the hypothesis that the SMM-BCS observations demonstrate Ñare-to-Ñare variations in the coronal calcium abundance. Figure 4 shows a histogram distribution of the results organized according to abundance value. The width of each bin is chosen to be approximately equal to the average root mean square (rms) uncertainty for determination of the A . The di†erently hatched areas correspond Ca from two active regions : Active Region to subsets of Ñares 2779 and Active Region 4474. The width of the distribution for entire sample is much larger than the rms error for determining the abundance for a given Ñare. In case of the Ñares observed from AR 2779 and AR 4474, the distribution of A is narrower than for the entire sample and their Ca di†er substantially. centroids 6.

FIG. 4.ÈDistribution of calcium abundance estimates for the studied Ñares. The width of a histogram bin corresponds approximately to the mean rms uncertainty for an individual abundance estimate. The width of the A distribution is over 6 times greater than the average uncertainty for Ca abundance estimate and indicates a substantial variation in the a single calcium compositionÈby over a factor of 3.5Èbetween Ñares. A systematic uncertainty of up to 20% may be assigned to the abundance scale. Di†erently hatched areas correspond to distributions of A for Ñares from Ca active regions AR 2779 (at lower values) and AR 4474 (at higher values).

DISCUSSION

A major result of this analysis is the Ðnding of a systematic Ñare-to-Ñare variation in the Ca XIX line-to-continuum ratio during the decay phases of Ñares, which we interpret as a variation in the coronal calcium abundance. Meyer (1985a, 1985b) pointed out that the abundances of low-FIP elements (less than 10 eV, such as calcium) are larger in the corona compared to the photosphere. As mentioned by Sterling et al. (1993), this suggests that the composition of the solar corona depends upon some mechanism that is acting on the ionized plasma, although there is no generally accepted mechanism to explain this phenomenon. The present results suggest that the situation is even more complicated and that the mechanism responsible for the variation of A for di†erent Ñares is time- and active Ca regionÈdependent. Solar cycle e†ects were investigated by comparing the average abundances recorded from Ñares observed in a single active region. Only active regions with four or more Ñares observed were considered. Table 2 shows the average

TABLE 1 ABSOLUTE CALCIUM ABUNDANCES A

Ca

FOR ANALYZED FLARES

Date/UT (1)

Active Region Number (2)

Location (deg) (3)

Ha (4)

GOES (5)

A ^1 p Ca (6)

N (7)

1980 Apr 7/01 : 08 . . . . . . . . 1980 Apr 7/05 : 41 . . . . . . . . 1980 Apr 8/03 : 07 . . . . . . . . 1980 Apr 10/09 : 22 . . . . . . 1980 Apr 13/04 : 08 . . . . . . 1980 Apr 30/20 : 25 . . . . . . 1980 May 7/14 : 57 . . . . . . . 1980 May 9/07 : 15 . . . . . . . 1980 May 21/21 : 05 . . . . . . 1980 Jun 4/09 : 11 . . . . . . . . 1980 Jun 13/22 : 34 . . . . . . . 1980 Jun 21/01 : 02 . . . . . . . 1980 Jun 24/15 : 24 . . . . . . . 1980 Jun 25/15 : 55 . . . . . . . 1980 Jun 29/02 : 38 . . . . . . . 1980 Jun 29/10 : 44 . . . . . . . 1980 Jun 29/18 : 26 . . . . . . . 1980 Jul 1/16 : 28 . . . . . . . . . 1980 Jul 5/22 : 45 . . . . . . . . . 1980 Jul 7/11 : 53 . . . . . . . . . 1980 Jul 11/22 : 18 . . . . . . . . 1980 Jul 12/11 : 21 . . . . . . . . 1980 Jul 12/16 : 00 . . . . . . . . 1980 Jul 12/17 : 38 . . . . . . . . 1980 Jul 12/19 : 25 . . . . . . . . 1980 Jul 12/19 : 33 . . . . . . . . 1980 Jul 13/06 : 33 . . . . . . . . 1980 Jul 13/14 : 34 . . . . . . . . 1980 Jul 13/17 : 33 . . . . . . . . 1980 Jul 13/18 : 03 . . . . . . . . 1980 Jul 13/19 : 19 . . . . . . . . 1980 Jul 13/19 : 22 . . . . . . . . 1980 Jul 13/19 : 32 . . . . . . . . 1980 Jul 14/01 : 52 . . . . . . . . 1980 Jul 14/08 : 27 . . . . . . . . 1980 Jul 15/22 : 48 . . . . . . . . 1980 Jul 17/06 : 11 . . . . . . . . 1980 Jul 20/19 : 26 . . . . . . . . 1980 Jul 21/03 : 00 . . . . . . . . 1980 Aug 23/21 : 30 . . . . . . 1980 Aug 24/16 : 12 . . . . . . 1980 Aug 24/16 : 35 . . . . . . 1980 Aug 25/13 : 05 . . . . . . 1980 Aug 31/12 : 49 . . . . . . 1980 Aug 31/12 : 52 . . . . . . 1980 Aug 14/06 : 14 . . . . . . 1980 Oct 20/18 : 34 . . . . . . . 1980 Nov 5/22 : 29 . . . . . . . 1980 Nov 5/22 : 34 . . . . . . . 1980 Nov 6/10 : 12 . . . . . . . 1980 Nov 6/11 : 25 . . . . . . . 1980 Nov 6/11 : 45 . . . . . . . 1980 Nov 6/12 : 36 . . . . . . . 1980 Nov 6/14 : 13 . . . . . . . 1980 Nov 6/15 : 26 . . . . . . . 1980 Nov 6/17 : 28 . . . . . . . 1980 Nov 7/04 : 47 . . . . . . . 1980 Nov 7/04 : 58 . . . . . . . 1980 Nov 7/09 : 41 . . . . . . . 1980 Nov 7/11 : 37 . . . . . . . 1980 Nov 7/14 : 41 . . . . . . . 1980 Nov 7/15 : 35 . . . . . . . 1980 Nov 7/15 : 37 . . . . . . . 1980 Nov 7/15 : 39 . . . . . . . 1980 Nov 7/22 : 30 . . . . . . . 1980 Nov 8/11 : 26 . . . . . . . 1980 Nov 8/16 : 19 . . . . . . . 1980 Nov 9/04 : 30 . . . . . . .

2372 2372 2372 2372 2372 2396 2418 2418 2456 2490 2502 2528 2522 2522 2522 2522 2522 2544 2550 2550 2562 2562 2562 2562 2562 2562 2562 2562 2562 2562 2562 2562 2562 2562 2562 2562 2562 2562 2562 2629 2629 2629 2629 2646 2646 2725 2744 2776 2776 2779 2779 2779 2779 2779 2779 2779 2779 2779 2779 2779 2779 2779 2779 2779 2779 2779 2779 2779

N10, E03 N12, E01 N12, W13 N12, W42 N10, W77 S13, W90 S22, W12 S21, W32 S14, W15 S13, E58 N17, E11 S12, E17 S29, W15 S29, W28 S27, W90 S27, W90 S20, W90 S12, W38 N28, W31 N26, W49 S10, E70 S14, E56 S10, E60 S09, E59 S12, E60 S14, E53 S13, E48 S15, E49 S10, E46 S09, E49 S13, E50 S13, E50 S13, E50 S10, E43 S13, E43 S15, E18 S12, E06 S19, W45 S14, W60 N16, W39 N17, W52 N17, W52 N18, W62 N12, E28 N12, E28 S09, W07 S17, E45 N11, E07 N10, E07 S11, E71 S13, E66 S12, E66 S09, E65 S09, E65 S09, E65 S09, E65 S11, E57 S11, E57 S06, E59 S11, E50 S07, E56 S07, E56 S07, E56 S07, E56 S10, E47 S15, E43 S08, E42 S09, E36

1B 1B 1B 1N 1F SN SB 1B 2B SB 1B 2N SB 1B ... 1F SN 1B 1B SB 2B SB 1B SB SN 1F SN SB SB SB SB SB SB SN 1B SB 1B 1B 1B 1B SB SB SB SB SB 3B SN ... 1B SF 1F SF ... ... 2B 2B ... SN SB SN SB SB SB SB 1N SB SN SB

M4 M8 M4 M4 M1 M2.2 C7 M7.2 X1.4 M4 ... M2 M1 M4.8 M3.6 M4.2 M4.2 X2.5 M8.9 M2 M5.3 M4.3 M3.2 C7 C5 C4 C4 C6 M2 C6 C9.2 C9.2 C9.2 C4.7 X1.1 C4.4 M3.4 M1.4 M8 M2.1 M1 ... M1 ... M2.8 X3.3 M1.0 ... M4.0 C7 C7 C9 M3.1 M3.1 X1.2 M4.2 ... M2.5 M1.2 M1.0 M4 ... C7.6 C7.6 M1 C6.2 C4.9 M1

5.70 ^ 0.09 5.51 ^ 0.07 6.49 ^ 0.12 6.82 ^ 0.16 6.44 ^ 0.16 6.22 ^ 0.15 7.30 ^ 0.51 6.37 ^ 0.10 5.94 ^ 0.07 7.09 ^ 0.10 6.21 ^ 0.46 5.79 ^ 0.11 6.27 ^ 0.26 6.43 ^ 0.33 6.91 ^ 0.14 7.30, 0.16 8.06 ^ 0.17 6.72 ^ 0.14 5.62 ^ 0.05 7.91 ^ 0.40 5.47 ^ 0.13 6.91 ^ 0.15 6.86 ^ 0.39 5.90 ^ 0.54 6.01 ^ 0.98 6.55 ^ 0.99 7.98 ^ 0.57 7.50 ^ 0.77 6.74 ^ 0.37 9.14 ^ 0.75 6.95 ^ 0.50 6.40 ^ 0.59 8.86 ^ 0.71 6.56 ^ 0.78 5.88 ^ 0.18 5.74 ^ 0.94 5.23 ^ 0.08 5.84 ^ 0.41 7.32 ^ 0.27 5.34 ^ 0.45 6.31 ^ 0.27 5.77 ^ 0.70 5.70 ^ 0.16 8.88 ^ 0.47 6.03 ^ 0.66 4.21 ^ 0.05 5.17 ^ 0.29 4.26 ^ 0.14 4.52 ^ 0.31 4.17 ^ 0.32 2.94 ^ 0.18 2.56 ^ 0.26 2.78 ^ 0.12 3.46 ^ 0.15 4.24 ^ 0.04 3.40 ^ 0.09 4.03 ^ 0.07 3.92 ^ 0.18 4.76 ^ 0.24 4.66 ^ 0.21 3.84 ^ 0.23 4.00 ^ 0.35 3.91 ^ 0.81 3.17 ^ 0.31 4.36 ^ 0.07 4.50 ^ 0.36 4.28 ^ 0.41 4.54 ^ 0.23

45 59 32 30 49 26 9 32 58 85 7 51 11 5 36 32 32 29 97 11 55 60 19 8 5 5 14 6 20 6 8 3 10 5 16 4 88 6 13 23 19 7 45 7 5 50 8 8 7 3 8 2 13 9 86 21 41 8 12 14 8 3 2 3 62 6 2 15

402

TABLE 1ÈContinued Date/UT (1) 1980 1980 1980 1980 1980 1980 1980 1980 1980 1980 1980 1980 1980 1980 1980 1980 1980 1980 1984 1984 1984 1984 1984 1984 1984 1984 1984 1984 1984 1984 1984 1984 1984 1984 1984 1984 1984 1984 1984 1984 1984 1984 1984 1984 1984 1984 1984 1984 1985 1985 1985 1985 1985 1985 1985 1985 1985 1985 1985 1985 1985 1985 1985 1985 1986 1986 1986 1986 1987

Nov 9/17 : 21 . . . . . . . Nov 10/08 : 12 . . . . . . Nov 10/09 : 37 . . . . . . Nov 11/06 : 29 . . . . . . Nov 11/10 : 32 . . . . . . Nov 11/15 : 17 . . . . . . Nov 11/15 : 54 . . . . . . Nov 12/02 : 51 . . . . . . Nov 12/08 : 10 . . . . . . Nov 12/09 : 24 . . . . . . Nov 12/11 : 06 . . . . . . Nov 12/17 : 04 . . . . . . Nov 12/17 : 37 . . . . . . Nov 12/23 : 35 . . . . . . Nov 13/01 : 03 . . . . . . Nov 18/14 : 55 . . . . . . Nov 19/05 : 44 . . . . . . Nov 22/05 : 38 . . . . . . Apr 25/00 : 22 . . . . . . Apr 25/00 : 57 . . . . . . Apr 26/09 : 03 . . . . . . Apr 27/05 : 40 . . . . . . Apr 29/02 : 50 . . . . . . Apr 29/07 : 44 . . . . . . Apr 30/05 : 57 . . . . . . Apr 30/12 : 13 . . . . . . May 1/01 : 34 . . . . . . . May 2/16 : 17 . . . . . . . May 2/19 : 25 . . . . . . . May 2/20 : 23 . . . . . . . May 2/20 : 58 . . . . . . . May 3/03 : 18 . . . . . . . May 5/01 : 07 . . . . . . . May 5/18 : 24 . . . . . . . May 6/01 : 45 . . . . . . . May 6/08 : 23 . . . . . . . May 6/16 : 25 . . . . . . . May 6/19 : 04 . . . . . . . May 19/21 : 55 . . . . . . May 20/01 : 29 . . . . . . May 20/03 : 01 . . . . . . May 20/03 : 02 . . . . . . May 20/05 : 42 . . . . . . May 20/22 : 53 . . . . . . May 20/23 : 11 . . . . . . May 21/17 : 47 . . . . . . May 21/18 : 10 . . . . . . May 22/15 : 01 . . . . . . Jan 20/20 : 51 . . . . . . . Jan 21/03 : 53 . . . . . . . Jan 21/14 : 19 . . . . . . . Jan 23/07 : 33 . . . . . . . Jan 23/07 : 43 . . . . . . . Jan 23/07 : 52 . . . . . . . Apr 24/01 : 52 . . . . . . May 2/08 : 19 . . . . . . . May 21/09 : 55 . . . . . . Jul 2/21 : 26 . . . . . . . . . Jul 7/05 : 28 . . . . . . . . . Jul 7/20 : 28 . . . . . . . . . Jul 9/02 : 10 . . . . . . . . . Jul 13/06 : 59 . . . . . . . . Jul 13/13 : 21 . . . . . . . . Oct 26/04 : 34 . . . . . . . Oct 7/10 : 56 . . . . . . . . Oct 19/00 : 46 . . . . . . . Oct 19/01 : 41 . . . . . . . Oct 24/12 : 40 . . . . . . . Apr 5/19 : 37 . . . . . . . .


Location (deg) (3)

Ha (4)

GOES (5)

A ^1 p Ca (6)

N (7)

2779 2779 2779 2779 2779 2779 2779 2779 2779 2779 2779 2779 2779 2779 2779 2779 2779 2793 4474 4474 4474 4474 4474 4474 4474 4474 4474 4474 4474 4474 4474 4474 4476 4474 4481 4481 4481 4481 4492 4492 4492 4492 4492 4492 4492 4492 4492 4492 4617 4617 4617 4617 4617 4617 4647 4647 4656 4671 4671 4671 4671 4671 4671 4698 4711 4750 4750 4750 4787

S11, E21 S12, E14 S15, E11 S12, E06 S12, E02 S12, W01 S12, W01 S13, W06 S12, W10 ... S12, W10 S14, W11 S13, W15 S13, W18 S11, W21 S10, W90 S10, W90 N12, W02 S12, E43 S11, E42 S09, E34 S10, E24 S13, E12 S17, E02 S14, W34 S12, W31 S14, W32 S14, W54 S11, W58 ... ... S12, W67 S11, W64 S11, W90 N06, E83 N07, E89 N08, E89 N05, E78 S10, E66 S10, E64 S13, E62 S13, E62 S08, E57 S08, E52 S06, E53 S06, E42 S08, E42 S09, E24 S09, W24 S10, W28 S09, W35 S10, W56 S11, W58 S11, W58 N05, E26 N03, W86 N05, E27 S14, E57 S15, E00 ... S13, W25 S17, W86 ... N06, W58 S11, W21 N23, E62 N23, E62 ..., ... S29, E90

SN 1B 1F SN 1N 1B SB 1B ... ... 1F 1B SN 1B 1B SB ... 2N 3B 2F 1B SB SN 1N 1B 2B 2B SB SB ... ... SB SF ... SF SB SB SN 2B 1B SB SB 1B 2B SN 1N 1B 2B 1B SN SN 1N 1N 1N 1N 1B SN 2B SN ... 1N SN ... 1N 2B 2N 2N ... SN

C5.3 M1.4 M1.5 M1.2 M3.6 M1 M2 M1.9 C8 C8 C8.6 M1.4 C7 M3 M9.4 M3.0 M6.0 C9.0 X10 ... M2.5 M2.3 C4.8 M1 M1.1 M2.3 M4.0 C7.9 M3.0 ... ... C7.1 C4.7 M7.5 C5 C3 C3.1 C3.8 X4.1 M2.9 M4.6 M4.6 M5.4 X10 X10. ... C9.7 M6.3 M4.1 M2.2 M2.4 ... M1.3 M1.3 C8.8 ... ... M4.5 C3.0 C2.7 ... C2.3 C2.0 M1.8 M5.2 M4.7 M4.7 C2.4 M1.1

3.92 ^ 0.21 4.37 ^ 0.11 4.05 ^ 0.11 4.69 ^ 0.24 4.70 ^ 0.47 5.37 ^ 0.46 4.50 ^ 0.14 4.66 ^ 0.11 4.01 ^ 0.23 3.79 ^ 0.35 5.49 ^ 0.33 5.27 ^ 0.37 4.52 ^ 0.25 4.29 ^ 0.24 4.38 ^ 0.06 5.64 ^ 0.13 5.26 ^ 0.10 4.82 ^ 0.26 5.99 ^ 0.14 5.28 ^ 0.08 7.02 ^ 0.17 5.04 ^ 0.19 6.61 ^ 0.24 9.39 ^ 0.57 6.88 ^ 0.20 7.47 ^ 0.20 6.70 ^ 0.10 6.58 ^ 0.20 6.31 ^ 0.10 6.73 ^ 0.40 6.99 ^ 0.43 7.83 ^ 0.34 8.38 ^ 0.53 7.84 ^ 0.10 9.60 ^ 0.68 5.58 ^ 1.36 10.2 ^ 1.44 9.44 ^ 0.59 3.93 ^ 0.04 6.64 ^ 0.13 6.33 ^ 0.10 5.01 ^ 0.32 6.20 ^ 0.12 5.35 ^ 0.10 4.76 ^ 0.09 6.06 ^ 0.29 5.43 ^ 0.12 5.19 ^ 0.13 5.15 ^ 0.08 4.95 ^ 0.13 6.80 ^ 0.41 6.01 ^ 0.31 5.86 ^ 0.21 6.94 ^ 0.39 6.32 ^ 0.23 6.11 ^ 0.12 5.54 ^ 0.53 6.75 ^ 0.10 4.29 ^ 0.44 5.87 ^ 0.61 5.60 ^ 0.27 5.76 ^ 0.50 6.23 ^ 0.64 6.46 ^ 0.25 5.75 ^ 0.16 5.61 ^ 0.23 6.28 ^ 0.17 4.99 ^ 0.68 4.99 ^ 0.51

8 19 29 8 3 14 13 45 5 3 18 14 10 5 85 29 32 10 10 69 20 9 39 9 41 64 96 31 37 22 18 18 12 31 11 2 3 11 65 38 40 9 35 47 22 14 24 15 40 15 14 9 11 6 14 60 3 39 3 3 8 3 2 23 18 9 32 3 3

403

404

SYLWESTER ET AL.

Vol. 501

TABLE 1ÈContinued Date/UT (1) 1987 1987 1987 1987 1987 1987 1987 1987 1987


Location (deg) (3)

Ha (4)

GOES (5)

A ^1 p Ca (6)

N (7)

4787 4790 4790 4790 4811 4811 4811 4811 4811

S28, E86 S30, W56 S30, W74 S30, W75 N30, W48 N30, W47 N29, W56 N28, W70 N29, W73

SN SN SN SN 2B 2B 1N 1N 1N

C9.2 C1.9 ... C2.8 ... M1.3 C5.9 C8.1 ...

5.65 ^ 0.45 5.61 ^ 1.15 4.63 ^ 0.76 5.52 ^ 0.55 4.54 ^ 0.50 4.79 ^ 0.71 5.51 ^ 0.60 4.96 ^ 0.74 5.20 ^ 0.65

10 2 3 11 4 7 5 5 8

Apr 6/04 : 33 . . . . . . . . Apr 17/02 : 38 . . . . . . Apr 18/14 : 37 . . . . . . Apr 18/14 : 58 . . . . . . May 25/03 : 43 . . . . . . May 25/03 : 48 . . . . . . May 25/18 : 56 . . . . . . May 26/20 : 00 . . . . . . May 26/20 : 22 . . . . . .

NOTE.ÈCol. (1) : Time of the Ñare maximum intensity as recorded by the BCS Ca XIX spectrometer. Col. (2) : NOAA active region number. Col. (3) : Heliographic coordinates from Solar-Geophysical Data, US Department of Commerce. Col. (6) : Values of A and the corresponding uncertainties have been multiplied by 106. Col. (7) : Number of individual ÑareCaspectra that are used to determine A . Ca

calcium abundance, A , for 10 di†erent active regions Ca 1984È1987. The standard deviobserved in 1980 and during ation to the mean value of A is labeled as 1 rms. The Ca active region is given in number of Ñares averaged in each the last column. These Ñares represent approximately 70% of our total sample. There does not appear to be a strong dependence on the average of A with activity cycle. The time-dependence of A Ca for Ñares observed from an individual active region was Ca examined in detail for the 10 active regions listed in Table 2. The column P gives the probability that a trend is not observed for the0Ñares in a particular region. A trend is not likely to be present in most of the cases except for AR 2779 and possibly AR 4474. For

these two cases, a slight increase is seen in the estimated A Ca as a function of time at the rate of 1.52 ] 10~7 day~1 and 1.48 ] 10~7 day~1 for AR 2779 and AR 4474, respectively. Figure 5 illustrates the trend for the abundance to increase for Ñares observed from AR 2779. Statistical tests were performed to check for signiÐcant di†erences in the average A between di†erent active Ca of a null hypothesis test regions. Table 3 presents the results

TABLE 2 AVERAGE CALCIUM ABUNDANCES BY ACTIVE REGIONS Active Region Number (1) 2372 2522 2562 2779 4474 4481 4492 4617 4671 4811

.......... .......... .......... .......... .......... .......... .......... .......... .......... ..........

Observing Period (2)

SA T ^ 1 rms Ca (3)

P (4)0

N (5)

1980 Apr 7È10 1980 June 25È29 1980 Jul 11È21 1980 Nov 6È19 1984 Apr 25ÈMay 5 1984 May 6 1984 May 19È22 1985 Jan 20È23 1985 July 2È13 1987 May 25È26

6.19 ^ 0.56 6.99 ^ 0.72 6.73 ^ 1.07 4.23 ^ 0.72 6.84 ^ 1.06 8.70 ^ 2.10 5.49 ^ 0.83 5.95 ^ 0.81 5.75 ^ 0.82 5.00 ^ 0.37

0.22 0.19 0.58 \0.01 0.04 0.72 0.90 0.25 0.88 0.42

5 5 19 36 15 4 10 6 6 5

NOTE.ÈCol. (3) : Values of A and the corresponding uncertainties Ca been multiplied by 106. Col. (5) : Number of Ñares included in average.

FIG. 5.ÈValues of A plotted for 36 Ñares observed from AR 2779 as a Ca for the abundance to increase with time, for this function of time. The trend active region, may be seen. The slope of a Ðtted line gives d(A )/dt \ 1.52 Ca ] 10~7 day~1.

TABLE 3 PROBABILITY OF CHANCE OCCURRENCE OF OBSERVED ABUNDANCE DISTRIBUTIONS FOR PAIRS OF ACTIVE REGIONS Active Region Number 2779 4811 4492 4671 4617 2372 2562 4474 2522

2779

4811

4492

4671

4617

2372

2562

4474

2522

4481

1.0

\0.01 1.0

\0.01 \0.01 1.0

\0.01 \0.01 0.6 1.0

\0.01 0.04 0.3 0.7 1.0

\0.01 \0.01 0.08 0.03 0.6 1.0

\0.01 \0.01 \0.01 0.03 0.06 0.1 1.0

\0.01 \0.01 \0.01 0.02 0.04 0.06 0.8 1.0

\0.01 \0.01 \0.01 0.02 0.04 0.06 0.5 0.6 1.0

0.02 0.04 0.05 0.06 0.07 0.09 0.02 0.2 0.2

No. 1, 1998


using a standard statistical analysis. The values represent the probabilities that two active regions are not distinguishable. Thus, low values indicate that the average abundances for the paired active regions are signiÐcantly di†erent. The table shows that there is a low probability of a chance occurrence of similar values of average A between the Ca paired active regions in most cases. The active region that has the largest di†erence from any other is AR 2779, and the Ñares with the smallest abundance estimates are all from this active region (also see Fig. 4). We note that this longitude was active for the preceding two solar rotations. Also examined was the possibility that the value of A Ca for an individual Ñare is correlated with other physical Ñare characteristics. In particular, the correlation between A Ca and various Ñare and active region characteristics were studied : 1. The Ha importance and the GOES soft X-ray classiÐcation ; 2. Area of the sunspots in the related active region ; 3. The duration, maximum, and total count rates recorded by the SMM Hard X-Ray Burst Spectrometer (Dennis et al. 1991) ; 4. Position of the Ñare in latitude and Carrington longitude ; 5. Center-to-limb dependence ; 6. Time and phase of the solar cycle ; 7. Peak calcium temperature and emission measure ; 8. Rise and decay characteristic times for calcium count rates, and calcium temperature and emission measure ; 9. Ratio of decay to rise times (asymmetry) for the above mentioned parameters. In no case was there a signiÐcant correlation detected. Figure 6 shows the values of A plotted against peak GOES Ca the GOES classiÐcation is X-ray Ñux for those Ñares where known. The mean value of the entire sample (5.77 ] 10~6) is indicated as well the photospheric value. Large Ñares have small scatter in values of A and are closer to the Ca average for the entire sample. The di†erences in the line-to-continuum measurements

405

have been interpreted in this work as evidence for a variation in the absolute calcium abundance on a Ñare-to-Ñare basis. Other possible causes for the variation in the observed ratio of F /F have been explored and are disw c cussed below. 6.1. Instrumental The SMM-BCS spectrometer was calibrated prior to launch and during the mission. Following the repair in 1984, the position gain in the calcium spectrometer began to change. The calibration results have been incorporated in the present analysis. Furthermore, the position gain does not a†ect the sensitivity of the detector (only its resolution), and so its e†ects are negligible for this study. We have compared the SMM-BCS spectra with calcium spectra from the solar Ñare X-rays (SOLFLEX) spectrometer (Feldman, Doschek, & Kreplin 1980) on the P78-1 spacecraft. The line spectra measured with the two instruments are very similar. The continuum of the SOLFLEX spectrometer is contaminated by germanium Ñuorescence, however, so the two cannot be directly compared (Sterling et al. 1993). 6.2. Plasma Opacity This present analysis is based on the intensity of the bright Ca XIX resonance line under the assumption that the thermal Ñare plasma is optically thin. If the plasma is not optically thin, then the intensity of the resonance line might be decreased relative to the continuum. The opacity at line center of a Doppler-broadened spectral line is given by (Sylwester et al. 1986b)

A

BA BA BA B S

N N N Jne2 k Ca XIX Ca H fj , (6) N N N mc 2RT Ca H e where f is the oscillator strength for the w resonance line, m and e are the electron mass and charge, respectively, l is the length, R is the ideal gas constant, and k is the atomic weight of calcium. For average Ñare conditions, if we assume T \ 15 MK, N /N \ 0.86, A \ 7 ] 10~6 Ca XIX Cawe take N Ca /N \ 0.85, and for the other quantities H e j \ 3.178 A , f \ 0.79, and k \ 40.08, then q \N l 0 e

q \ (2.4 ] 10~22)N l . (7) 0 e A typical Ñaring loop has a length of 2 ] 109 cm and a diameter that is 10 times smaller. Thus, if the line of sight is across the loop (perpendicular to the long axis of the loop), then for a density of N \ 5 ] 1011 cm~3, we have q \ e 0 0.024. The longest possible distance is one-half the loop length, which results in q \ 0.12. This is an extreme case, since Ñare loops normally0 have a temperature distribution with the hottest material at the loop top, and the peak in the Ca XIX emissivity function, f (T ) (see eq. [3]), occurs at i line w will preferentially be around 35 MK. Observations of weighted toward the hot material near the loop top. Therefore, it can be concluded that opacity e†ects will be much less than 10%, and thus, this cannot be the reason for the observed variation in the line-to-continuum intensity ratio.

FIG. 6.ÈValues of A plotted against peak GOES X-ray Ñux for those Ca classiÐcation is known. The upper horizontal Ñares for which the GOES line indicates the mean value of A of the entire sample of this analysis, Ca the photospheric value. and the lower horizontal line indicates

6.3. Nonequilibrium Ionization The e†ects of transient ionization in solar Ñare plasma have been studied in a number of papers (Mewe & Schrijver 1980 ; Sylwester, Mewe, & Schrijver 1980a ; Mewe et al. 1985). If the plasma is not in thermal equilibrium, it is more

406

SYLWESTER ET AL.

difficult to interpret the observed X-ray spectrum. A detailed interpretation requires solving a coupled set of differential equations with time-dependent coefficients that vary with temperature and density. Under certain conditions, this can be simpliÐed. For example, for the time during which a plasma is being heated, the characteristic time for ionization becomes important, whereas when the plasma is cooling, the recombination time should be considered. Mewe (1984) considered the ionization and recombination times as a function of temperature. These results are given in Table 4 for Ca XIX. The temperature decay times for Ñares in this study were 5 minutes or more. For densities 1011 cm~3 \ N \ 1012 e cm~3, which are typical for Ñare plasmas after the maximum (Wolfson et al. 1983 ; Sylwester et al. 1986a), q rec is of order 30 s or less, i.e., several times less than observed. Thus, the Ñare plasma can be considered in quasiequilibrium during Ñare decay, and transient ionization e†ects can be considered unimportant for the purposes of this study. Spectra acquired during the Ñare rise phase were not included in this study. 6.4. Abundance Depletion of All Elements Except Calcium The calculated continuum (eq. [4]) at 3.178 A depends weakly on the heavy elemental composition of the emitting plasma. The main e†ect from heavy elements comes from recombination of oxygen, neon, magnesium, and silicon. In order to test the e†ect of abundances on the solar thermal continuum, a computation was made assuming that all elements other than Ca and H had zero abundances. The e†ect on the computed F /F intensity ratio was less than 60%, c as an explanation for the observed and this can be ruledw out line-to-continuum variations. We can not rule out the possibility that the continuum has been a†ected by increases in non-Ca elemental abundances, such as helium, but this would not account for the observation of enhanced values of A relative to photospheric values. Ca 6.5. Multithermal Plasma Typical Ñare plasmas are multithermal, with temperature ranges extending to over 25 MK (see, e.g., Fludra & Schmelz 1995). The e†ect of multithermal plasma on the line-to-continuum analysis has been investigated by assuming the following form for the di†erential emission measure distribution to be r(T ) \ const. for 6 MK \ T \ 25 MK. The Ca XIX line and continuum Ñuxes were calculated for this broad di†erential emission measure distribution. The resulting line Ñuxes were used to derive temperature and the calcium abundance of the simulated spectrum assuming an isothermal approximation. Checking this result shows that the isothermal approximation introduces an error in the abundance determination that is less

TABLE 4 IONIZATION AND RECOMBINATION TIMES (IN s cm~3) FOR THE CA XIX ION AT DIFFERENT TEMPERATURES T (MK) PARAMETER

8

15

25

N ]q ...... Ne ] qion . . . . . . e rec

8.6 ] 1010 2.0 ] 1012

2.7 ] 1010 2.8 ] 1012

1.4 ] 1010 3.6 ] 1012

Vol. 501

than 5%. Furthermore, Fludra et al. (1991) have calculated A for 12 Ñares from Table 1 using a method of multiCa thermal analysis to obtain calcium abundances. Their results were the same, to within 3%, as those obtained from an isothermal analysis, which addresses the concern raised in Phillips & Feldman (1991). 7.

SUMMARY

This paper presents Ðnal, detailed results of the study of variations in the line-to-continuum ratio in vicinity of the w line of Ca XIX ion using soft X-ray spectra from the BCS aboard the SMM satellite. The analysis of thousands of spectra obtained during decay phases of more than 100 stronger Ñares revealed the presence of systematic di†erences in the line-to-continuum ratio between Ñares. This di†erence has been interpreted in terms of the varying Ca abundance hypothesis. Detailed considerations have ruled out other possible interpretations of the observed Ñare-to-Ñare variations of this ratio. The results obtained fully conÐrm the discovery of variations of coronal plasma composition from spectroscopic measurements (Sylwester et al. 1984). This discovery led to what is now one of the fastest growing areas of interest in solar physicsÈspectroscopic X-ray and EUV determinations of coronal plasma composition. In this paper, absolute (relative to hydrogen) estimates of Ca abundance are given for Ñares observed during the period 1980È1987 by the BCS on the SMM spacecraft. The following conclusions may be drawn from this study : 1. Average Ñare calcium abundance (5.77 ] 10~6) is more than twice the photospheric value. 2. Flare-to-Ñare di†erences may amount to factor of D3.5 ; the lowest Ñare abundance determined corresponds to the photospheric value (2.6 ] 10~6). 3. For most of Ñares, Ca abundance does not change during decay phase evolution. 4. Observed A variations do not correlate with any of Ca used Ñare and/or active region characthe many commonly teristics, except for the time trend seen for AR 2779. 5. For a particular active region, Ñare calcium abundances are similar ; however, they may di†er substantially from the abundances of Ñares for other active regionsÈthe active region e†ect is clearly pronounced. The observed pattern of Ñare abundance variations does not contradict the FIP-biased mechanism of coronal enrichment. As expected, the absolute abundance of Ca (a low-FIP element) in the corona is higher than in the photosphere. However, the time trend and active region e†ect of the present results impose substantial new limitations on the theoretical models of physical processes responsible for buildup of di†erences of the coronal plasma composition. Recently, we (Bentley et al. 1998) have performed analyses of the Ñares observed with the BCS on the Y ohkoh spacecraft. In this study, we considered more than 170 Ñares and have determined that for this group A \ 3.64 ] 10~6, which is closer to the photospheric value.CaA comparison of the SMM and Y ohkoh data is in progress in order to evaluate the signiÐcance of these results. The X-Ray Polychromator experiment was a collaborative program between Lockheed Palo Alto Research Laboratory, USA, the Mullard Space Science Laboratory,

No. 1, 1998


UK, and the Rutherford Appleton Laboratory, UK. The authors thank Professor J. L. Culhane for useful discussions. J. S. acknowledges support for a part of this investigation from the British Council. J. R. L. acknowledges support from the Lockheed Martin Independent Research

407

Program. R. D. B., A. F., and M.-C. Z. acknowledge support from the UK Science and Engineering Research Council and the Particle Physics and Astrophysics Research Council.

REFERENCES Acton, L. W., et al. 1980, Sol. Phys., 65, 53 McGuire, R. E., von Rosevinge, T. T., & McDonald, F. B. 1985, ApJ, 301, Allen, C. W. 1973, Astrophysical Quantities (3d ed. ; London : Athlone) 938 Antonucci, E., et al. 1982, Sol. Phys., 78, 107 Meyer, J. P. 1985a, ApJS, 57, 151 Arnaud, J. 1984, Proc. Fourth European Meeting on Solar Physics (ESA ÈÈÈ. 1985b, ApJS, 57, 173 SP-220) (Paris : ESA), 115 ÈÈÈ. 1993, Adv. Space Res., 13(9), 377 Athay, R. G. 1986, Physics of the Sun, Vol. 2, ed. P. A. Sturrock Mewe, R., & Schrijver, J. 1980, A&A, 87, 261 (Dordrecht : Reidel), chap. 8 Mewe, R. 1984, Physica Scripta, T7, 5 Bely-Dubau, F., et al. 1982, MNRAS, 201, 1155 Mewe, R., Gronenshild, E. H. B. M., van den Oord, G. H. J., & Lemen, J. R. Bentley, R. D., Sylwester, J., & Lemen, J. R. 1997, Adv. Space Res., 20, 2275 1986, A&AS, 65, 511 Dennis, B. R., et al., eds. 1991, NASA Technical Memorandum 4332 : The Mewe, R., Lemen, J. R., Peres, G., Schrijver, J., & Serio, S. 1985, A&A, 152, Complete Hard X-Ray Burst Spectrometer Event Listing 1980È1989 229 (Washington DC : NASA) Parmar, A. N., Culhane, J. L., Rapley, C. G., Antonucci, E., Gabriel, A. H., Feldman, U. 1992, Physica Scripta, 46, 202 & Loulergue, M. 1981, MNRAS, 197, 29P Feldman, U., Doschek, G. A., & Kreplin, R. W. 1980, ApJ, 238, 365 Parkinson, J. H. 1977, A&A, 57, 185 Fludra, A., Bentley, R. D., Culhane, J. L., Lemen, J. R., & Sylwester, J. 1991, Phillips, K. J. H., & Feldman, U. 1991, ApJ, 379, 401 Adv. Space Res., 11(1), 155 Pottash, S. R. 1964, Space Sci. Rev., 3, 816 Fludra, A., Culhane, J. L., Bentley, R. D., Doschek, G. A., Hiei, E., Phillips, Sterling, A., Doschek, G. A., & Feldman, U. 1993, ApJ, 404, 394 K. J. H., Sterling, A., & Watanabe, T. 1993, Adv. Space Res., 13(9), 395 Stone, E. C. 1989, in AIP Conf. Proc. 183, Cosmic Abundances of Matter, Fludra, A., Lemen, J. R., Jakimiec, J., Bentley, R. D., & Sylwester, J. 1989, ed. C. J. Waddington (New York : AIP), 72 ApJ, 344, 991 Strong, K. T. 1988, XRP Team Final Report : Contract NAS5-28713 Fludra, A., & Schmelz, J. T. 1995, ApJ, 447, 936 Sylwester, B., Farnik, F., Sylwester, J., Jakimiec, J., & Valnicek, B. 1986a, Geiss, J. 1982, Space Sci. Rev., 33, 201 Adv. Space Res., 6(6), 233 Geiss, J., & Bochsler, P. 1986, in The Sun and the Heliosphere in Three Sylwester, B., et al. 1986b, Sol. Phys., 103, 67 Dimensions, ed. R. G. Marsden (Dordrecht : Reidel), 173 Sylwester, J., Lemen, J. R., & Mewe, R. 1984, Nature, 310, 665 Lemen, J. R., Phillips, K. J. H., Cowan, R. D., Hata, J., & Grant, I. P. 1984, Sylwester, J., Mewe, R., & Schrijver, J. 1980a, A&AS, 40, 335 A&A, 135, 313 Sylwester, J., Schrijver, J., & Mewe, R. 1980b, Sol. Phys., 67, 285 Lemen, J. R., Sylwester, J., & Bentley, R. D. 1986, Adv. Space Res., 6(6), 245 Veck, N. J., & Parkinson, J. H. 1981, MNRAS, 197, 41 Lemen, J. R., Sylwester, J., Bentley, R. D., & Fludra, A. 1998, in Widing, K. G., & Feldman, U. 1989, ApJ, 344, 1046 preparation Wolfson, J., Doyle, J. G., Leibacher, J. W., & Phillips, K. J. H. 1983, ApJ, Mariska, J. T. 1980, ApJ, 235, 268 269, 319 Mason, H. E. 1975, MNRAS, 171, 119